So even postive integers are by defention in form 2k where k is a natural number so
let the sum of even integers to n=S
S=2(1+2+3+4+5+6+7+8+......+k-1+k
divide bith sides of equation 1 by 2
0.5S=1+2+3+4+5+...........+k-1+k
S=2(k+(k-1)+..............................+2+1)
divide both sides of equation 2 by 2
0.5S=k+k-1+..............................+2+1)
by adding both we will get
___________________________
S=(k+1)(k)
so the sum will be equal to
S=

so let us test the equation
for the first 3 even number there sums will be
2+4+6=12
by our equation 3^2+3=12
gave us the same answer so our equation is correct
In the expression, the real number a equals 12 and the real number b equals -16.
<h3>How to explain the information?</h3>
It should be noted that the expression given is:
= (4 - 2i)²
Therefore, we need to expand the expression. This will be:
= (4 - 2i)(4 - 2i)
= 16 -8i -8i + 4i²
= 16 -16i +4i²
Substitute -1 for i²
= 16 - 16i + 4(-1)
= 16 - 16i - 4
= 12 - 16i
Therefore, the value of the expression is 12 - 16i.
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Evaluate the expression ( 4 − 2 i )² and write the result in the form a + b i.
I think the answer would be B
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